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- Title
Study of several probability distribution functions for the Klein–Kramers equation.
- Authors
Li, Yaxi; Kai, Yue
- Abstract
In this paper, we take variable separation method to study Klein–Kramers (KK) equation. By choosing different eigenvalues and noise functions, we can get different probability density functions (PDFs) of KK equation. These PDFs contain not only normal distributions but also other distributions that correspond to anomalous diffusion phenomena. For example, power-law distribution, truncated Cauchy–Lorentz distribution, Weibull distribution, log-logistic distribution, Gamma distribution. We also show the 3D and 2D profiles of these PDFs to analyze the corresponding dynamic properties and illustrate the possible practical applications of these results. In addition, we also find some exact solutions that are not PDFs. They are also listed to ensure the completeness of the results and to illustrate the potential applications of these exact solutions.
- Subjects
WEIBULL distribution; POWER law (Mathematics); GAUSSIAN distribution; EQUATIONS; GAMMA distributions; SEPARATION of variables; DISTRIBUTION (Probability theory); PROBABILITY density function
- Publication
Modern Physics Letters B, 2024, Vol 38, Issue 24, p1
- ISSN
0217-9849
- Publication type
Article
- DOI
10.1142/S0217984924502129